If a brake caliper was dragging he should have excessive brake dust on one wheel, the smell of hot brakes after driving and a slightly more sluggish vehicle that doesn't coast like it usually does and it should probably be pulling to one side. If none of these are happening, I would start with rotating and balancing the tires. Cheap and easy first.

A little update, seems to be either a fuel supply or firing issue. Not overheating or anything to do with brakes or tires. After warm up is when it starts. I had the front coil pack replaced before this happened, so I had original coil pack back in. The original coil pack has rough idle, in gear, after warmup. Not sure if it is two separate problems. Maybe a stuck injector, and a firing issue???? Hopefully one of you guys with the experience can help me out. Thank you in advance

Re: Vibration on acceleration-'03 DTS

As stated, check for codes first. Something like this would typically throw a code.

I'd run a bunch of fuel injector cleaner for your next couple of tanks, and perhaps replace fuel filter too. Also maybe check/replace air filter and spark plugs. Plus, I'd clean the throttle body real good. You can do all this yourself, for not much money or time.